Presentation Title

Characterizing Parallelograms with Sides and Diagonals Having Integer Lengths

Presenter Information

Amanda R. PetrowFollow

Presentation Type

Oral Presentation

School

School of Sciences and Social Sciences

Discipline

Mathematics

Mentor

Vincent Ferlini

Date & Time

April 9th at 10:15 AM - 11:15 AM

Location

David F. Putnam Science Center, Room 102

Abstract

A perfect parallelogram is defined as a parallelogram whose sides and diagonals are positive integers. We first look at three separate cases one of which is a general parallelogram where the sides and diagonals satisfy the parallelogram equation. The second case is a perfect rational parallelogram where the sides and diagonals are positive rational numbers. Then the third case is a perfect parallelogram. The use of up to scaling on each of the above parallelograms is used to make the observation that all perfect parallelograms have a parameterization. We then look at the special case of each of the above in which a perfect rectangle is obtained.

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Apr 9th, 10:15 AM

Characterizing Parallelograms with Sides and Diagonals Having Integer Lengths

David F. Putnam Science Center, Room 102

A perfect parallelogram is defined as a parallelogram whose sides and diagonals are positive integers. We first look at three separate cases one of which is a general parallelogram where the sides and diagonals satisfy the parallelogram equation. The second case is a perfect rational parallelogram where the sides and diagonals are positive rational numbers. Then the third case is a perfect parallelogram. The use of up to scaling on each of the above parallelograms is used to make the observation that all perfect parallelograms have a parameterization. We then look at the special case of each of the above in which a perfect rectangle is obtained.